After initially mentioning here that my ThinkPad X40 had no suspend issues on Fedora 14, the reported issues with suspending on that hardware have sporadically started to occur. I don't know why it works sometimes and not other times, unless a recent software update stuffed something up.
Fortunately I have a solution! If your ThinkPad X40 doesn't come out of standby, hold the power button, then hit a random number of keys for upwards of 20 seconds. That seems like a long time and the screen remains dark the entire time, but eventually it wakes up.
Arch Linux never did this on this machine, so I'm thinking its a Red Hat issue, or maybe the latest kernel doesn't like this machine either. Oh well, se a vida é.